1. 1 Heavy quark Potentials in Full QCD Lattice Simulations at Finite Temperature Yuu Maezawa (The Univ. of Tokyo) Tsukuba-Tokyo collaboration Univ. of Tsukuba S. Aoki K. Kanaya Y. Taniguchi E. Ejiri T. Hatsuda N. Ishii N. Ukita The Univ. of Tokyo

2. 2 Contents Motivations Free energy and Potential on lattice Numerical simulations Summary  Potentials using two-flavor Wilson quarks  Screening effect  Comparison with Staggered fermion

3. 3 Motivations  Heavy quark free energy in hot matter  Full-QCD lattice simulation We use improved Wilson fermion action. 1. Channel dependence of "potential" ( 1 c, 8 c, 3 c, 6 c ) 2. Effective running coupling at 3. Debye screening mass at 4. Relation to p-QCD at high T 1. not many works 2. Comparison with staggered fermion action

4. 4 Free energy and Potential on a lattice McLerran, Svetitsky, PRD 24 (1981) 450 Free energy of the quark-antiquark pair Static charged quark Quark- antiquark “potential” (normalized free energy) Polyakov loop:

5. 5 Projection operator and Nadkarni, PRD 34 (1986) 3904 Quark-quark potential  Separation to each channel after Coulomb gauge fixing

6. 6 Numerical simulations Lattice size: Gauge action: RG Iwasaki improved action Fermion action: Clover improved Wilson action (2-flavor) Quark mass & Temperature # of Configurations: 500 confs. (5000 traj.) Gauge fixing: Coulomb gauge Parameters

7. 7 1 c channel: attractive force 8 c channel: repulsive force Quark-antiquark potential Debye Screening

8. 8 3 c channel: attractive force 6 c channel: repulsive force Quark-quark potential Debye Screening c.f. Quenched action Nakamura and Saito (2004)

9. 9 : Casimir factor Fitting the potentials of each channel with and as free parameters. Screening effect Phenomenological potential : screened Coulomb potential

10. 10 For T > 2.5Tc, potentials of each channel can be written by the same parameters: and. Results of and.

11. 11 Relation between and. is described by effective running coupling with 10% accuracy.  Effective running coupling  Screening mass ? for 1 c potential 10%

12. 12  Leading order perturbation  2-loop running coupling on a lattice vs. perturbative screening mass Lattice screening mass is not reproduced by the LO-type screening mass.

13. 13 Magnetic screening mass:  Next-to-leading order perturbation Rebhan, PRD 48 (1993) 48 on a lattice vs. perturbative screening mass Lattice screening mass is well reproduced by the NLO-type screening mass at T > 2Tc. Fitting

14. 14 Comparison with staggered fermion Kaczmarek and Zantow, PRD 71 (2005) 114510  Improved staggered fermion with Systematic error due to the difference of actions smaller when

15. 15  Heavy quark "potential" Lattice QCD simulation using 2-flavor Wilson fermion action Summary  Screening effect potentials are fitted by and are independent on channel. 1 c, 3 c : attractive force 8 c, 6 c : repulsive force effective running coupling 2-loop running coupling  Systematic error due to the difference of actions smaller when